Elementary Linear Algebra
Elementary Linear Algebra
8th Edition
ISBN: 9780357156100
Author: Ron Larson
Publisher: Cengage Limited
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Chapter 7.2, Problem 46E

Guide Proof Prove nonzero nilpotent matrices are not diagonalizable

Getting started: From Exercises 80 in Section 7.1, you know that 0 is the only eigenvalue of the nilpotent matrix A. Show that it is impossible for A to be diagonalizable.

(i) Assume A is diagonalizable, so there exists an invertible matrix P such that P − 1 A P = D , here D is the zero matrix.

(ii) Find A in term of P , P − 1 and D.

(iii) Find a contradiction and conclude that nonzero nilpotent matrices are not diagonalizable.

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Chapter 7.2, Problem 45E
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Chapter 7 Solutions

Elementary Linear Algebra

Ch. 7.1 - Verifying Eigenvalues and Eigenvectors in...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and Eigenvectors in...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Determining Eigenvectors In Exercise 9-12,...Ch. 7.1 - Determining Eigenvectors In Exercise 9-12,...
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